\[ \int \frac {80 e^{-2 e^5+2 x}+40 e^{-e^5+x} \log (5)+5 \log ^2(5)+e^{\frac {5 e^{-e^5+x}+2 e^{-e^5+x} \log (\log (4))}{4 e^{-e^5+x}+\log (5)}} \left (5 e^{-e^5+x} \log (5)+2 e^{-e^5+x} \log (5) \log (\log (4))\right )}{16 e^{-2 e^5+2 x}+8 e^{-e^5+x} \log (5)+\log ^2(5)} \, dx \]
Optimal antiderivative \[ 5 x +{\mathrm e}^{\frac {5+\ln \left (4 \ln \left (2\right )^{2}\right )}{\ln \left (5\right ) {\mathrm e}^{{\mathrm e}^{5}-x}+4}} \]
command
integrate(((log(5)*exp(-exp(5)+x)*log(4*log(2)^2)+5*log(5)*exp(-exp(5)+x))*exp((exp(-exp(5)+x)*log(4*log(2)^2)+5*exp(-exp(5)+x))/(4*exp(-exp(5)+x)+log(5)))+80*exp(-exp(5)+x)^2+40*log(5)*exp(-exp(5)+x)+5*log(5)^2)/(16*exp(-exp(5)+x)^2+8*log(5)*exp(-exp(5)+x)+log(5)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ {\left (5 \, x e^{x} + 5 \, e^{x} \log \left (4 \, e^{\left (x - e^{5}\right )} + \log \left (5\right )\right ) - 5 \, e^{x} \log \left (-4 \, e^{\left (x - e^{5}\right )} - \log \left (5\right )\right ) + e^{\left (\frac {4 \, x e^{\left (x - e^{5}\right )} + x \log \left (5\right ) + 2 \, e^{\left (x - e^{5}\right )} \log \left (2\right ) + 2 \, e^{\left (x - e^{5}\right )} \log \left (\log \left (2\right )\right ) + 5 \, e^{\left (x - e^{5}\right )}}{4 \, e^{\left (x - e^{5}\right )} + \log \left (5\right )}\right )}\right )} e^{\left (-x\right )} \]